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Millimeter wave technology is an essential component of most solutions that address the coverage and throughput demands of next-generation cellular networks. To overcome the high propagation losses however, it is necessary to deploy large antenna arrays for spatial localization of energy by beamforming. This imposes a significant communication overhead, especially when channel reciprocity does not hold. In this work, we study the problem of successive one-bit feedback-assisted beam alignment. We exploit the sparse nature of the millimeter wave channel to pose the beamforming problem as a questioning strategy. We consider both adaptive ( closed-loop ) and non-adaptive ( open-loop ) channel sounding techniques which are robust to erroneous feedback signals caused by noisy quantization. In the adaptive case, we formulate new sounding signals by drawing a parallel with the well known Ulam's problem. In the non-adaptive case, the beams are designed in accordance to an open-loop code. We demonstrate that multiple paths can also be resolved by using ideas from group testing. Finally, we show the efficacy of our proposed techniques via simulations.
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